Basic Set Theory (Cartesian Products): a simple exercise.

Hey guys! I'm brand new to set theory; I just started learning it as a hobby. I just finished the section on cartesian products, and I'm a bit hung up on one of the exercises.

Let A,B,X, and Y be sets. A contains X, and B contains Y.

Prove that C(XxY) = AxC(Y) U C(X)xB

Mendelson's Intro to Topology was a bit vague on what the complement of a cartesian product would be (and by a bit vague, I mean completely silent). I'm guessing that C(XxY) would = {(q_{1},w_{1)},(q_{2},w_{2}),...(q_{n},w_{n})} where q is not in X and w is not in Y, yes?

Re: Basic Set Theory (Cartesian Products): a simple exercise.

Re: Basic Set Theory (Cartesian Products): a simple exercise.

Lets see, if X and Y are sets, then is the set of all 2 tuples (x, y) where **AND** . Now the logical negation of the statement is . Which means that **atleast** one of the statements have to be true. So either or or and have to be true. So we have the union of 3 sets. The first case, if is true. Now it dosent matter where y is in, it can be anywhere in its universe, since the we only care about the statement . So the first cartesian product is . The next case is if is true. Then it does not matter where x is in its universe, which is A, so the second cartesian product is . Now the third case is if both statements are true. and . which means . So . Notice that So, we have only

Re: Basic Set Theory (Cartesian Products): a simple exercise.

Quote:

Originally Posted by

**Plato** I find this post almost unreadable.

I apologize, I don't yet know how to use the LaTex programming. I'll go check out the help forum.